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The logician 's dictum that in many cases we can say, the meaning is the use. Most contemporary logicians prefer to think that the Introduction Rule s and the Elimination Rules for an expression are equally important. In this case, ''and'' is characterized by the following rules: An apparent problem with this was pointed out by ). These constraints are what Dummett was referring to. Harmony, then, referes to certain constraints that a proof theory must let hold between introduction and elimination rules for it to be meaningful, or in other words, for its inference rules to be meaning-constituting. The application of harmony to logic may be considered a special case; it makes sense to talk of harmony with respect to not only inferential systems, but also conceptual systems in human cognition, and to type systems in programming languages. Semantics of this form has not provided a very great challenge to that sketched in Tarski's Semantic Theory Of Truth , but many philosophers interested in reconstituting the semantics of logic in a way that respects Ludwig Wittgenstein 's ''meaning is use'' have felt that harmony holds the key. EXTERNAL LINKS
REFERENCES Prior, Arthur. "The runabout inference ticket." ''Analysis'', 21, pp38-39, 1960-61. Belnap, Nuel D. Jr. "Tonk, Plonk, and Plink", ''Analysis'', 22, pp130-134, 1961-62. |
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